Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section.
Multiple-input multiple-output (MIMO) communication systems employ multiple transmit antennas and multiple receive antennas to communicate data symbols over a communications channel. MIMO communication systems may allow a plurality of mobile stations to be serviced utilizing a same frequency band. In this manner, MIMO communication systems may advantageously increase an amount of data the communication systems is able to send to users.
MIMO systems may find use in a variety of applications including, but not limited to, wireless networks, cellular systems including 3G and 4G systems, such as 3GPP LTE-Advanced, local and wide area networks, and wireless broadband systems (such as WiMAX).
Generally, a transmitter in a MIMO system may have a plurality of antennas, designated mathematically by Nt and a plurality of mobile stations, U. The mobile stations U may each have a single antenna for receipt of data over the communications channel. The transmitter, which may be implemented as a base station, may be configured to simultaneously transmit one symbol for each of the mobile stations. Each mobile station may receive signals using one or a plurality of receive antennas.
The communications channel, however, may introduce a variety of non-idealities to a transmitted signal, such as may be caused by multipath interference, reflections, motion of one or more mobile stations, or other properties of a communications channel. A vector of transmit messages to be transmitted over the communications channel may be represented by a vector s=[s1 . . . sU]T, where T denotes a transposition operation. The transmitter may generate precoded data symbols, mathematically denoted x, from the transmit messages s based on channel state information corresponding to the communications channel.
In a communications channel that may generally be considered a slowly varying frequency flat fading channel, a vector of signals y received by the U antennas may then be expressed as y=Hx+n. Where H is a channel matrix corresponding to the communications channel and n is a noise vector. The channel matrix generally refers to a matrix of data which may represent the operation of the communications channel on the transmitted data symbols, including representations of such effects as reflections.
The channel matrix may be reconstructed to form a real-valued equivalent channel matrix Hr. If  and ℑ are used to denote the real and imaginary parts of an argument, respectively, the signal vectors y may be rewritten as:
      [                                                    ⁢                                                  ⁢            y                                                                        ⁢                                                  ⁢            y                                ]    =                    [                                                                            ⁢                                                                  ⁢                H                                                                                      -                                                  ⁢                                                                  ⁢                H                                                                                                        ⁢                                                                  ⁢                H                                                                                    ⁢                                                                  ⁢                H                                                    ]            ⁡              [                                                                            ⁢                                                                  ⁢                x                                                                                                        ⁢                                                                  ⁢                x                                                    ]              +          [                                                                ⁢                                                          ⁢              n                                                                                        ⁢                                                          ⁢              n                                          ]      
The real-valued equivalent system model of the signals y may be written yr=Hrxr+nr.
To generate the precoded data symbols x, channel inversion techniques may be used. Channel inversion techniques have been described, for example, in C. Peel, et. al., “A vector-perturbation technique for near-capacity multiantenna muhiuser communication—part I: channel inversion and regularization,” IEEE Intl. Symp. on Circuits and Systems (ISCAS), 2007, pp. 673-676, which is hereby incorporated by reference in its entirety for any purpose. Channel inversion techniques may generate the precoded data symbols xr in accordance with an equation xr=(Prsr)/√γ where Pr=H*r(HrH*r)−1, the pseudo inverse of the real-valued equivalent channel matrix Hr, and γ=∥Prsr∥2 where ∥ ∥ denotes the 2-norm of the enclosed argument. γ therefore may be considered a power normalization factor, which ensures the total transmit energy vector has a unitary magnitude. In this manner, channel inverse techniques generally alter transmit messages using an inverse of the channel matrix.
Vector perturbation techniques may also be used to generate the precoded data symbols. Vector perturbation techniques are described, for example, in B. Hochwald, et. al., “A vector-perturbation technique for near-capacity multiantenna multiuser communication—part II: perturbation,” IEEE Trans. Commun., vol. 53, no. 3, pp. 637-544, 2005, which is hereby incorporated by reference in its entirety for any purpose. Vector perturbation techniques may perturb the transmit messages by a scaled integer vector. Vector perturbation may be applied in combination with channel inversion techniques, described above, such that the precoded data symbols xr may be expressed as xr=(Pr/√γ)(sr+τlr) where τ is a fixed scalar value, and lr is a 2U-dimensional vector with integer entries. The normalization factor for maintaining unit transmit energy may now be given by γ=∥Pr(sr+τlr)∥2. There are a variety of methods and considerations for selecting the scalar τ and vector lr, described for example in B. Hassibi et. al., “On the sphere-decoding algorithm I. Expected complexity,” IEEE Trans. Signal Process., vol. 53, no. 8, pp. 2806-2818, 2005 and C. Windpassinger, et. al., “Lattice-reduction-aided broadcast precoding,” IEEE Trans. Commun., vol. 52, no. 12, pp. 2057-2060, 2004, both of which are incorporated by reference herein in their entirety and for any purpose.